On the scattering theory and the singular perturbations for the self-adjoint operators

关于散射理论和自伴算子的奇异摄动

基本信息

批准号：
14540183
负责人：
WATANABE Kazuo
金额：
$ 2.11万
依托单位：
Gakushuin University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2002
资助国家：
日本
起止时间：
2002 至 2003
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-14540183/
关键词：
Maxwell Shrodinger Self-adjoint Navier-Stokes Singular Perturbation Besov space Bi-harmonic Dissipative 消散型最大関数 Wiener空間

项目摘要

1. The H-2-construction to treat the singular perturbation for the self-adjoint operator by the operator theoretical method has been studied by K. Watanabe. The author obtains some results for the operator, for example, necessary and sufficient condition of the existence of embedded eigenvalues, representation of the scattering matrix and etc.2. The regularity of the solutions for the Maxwell, Stokes and Navier-Stokes equation with the interface has been investigated by K. Watanabe. Especially the following results is remarkable : if the tangential component does not have the singularity, then the regularity of the solution gains rank one.3. The partial differential equation with the dissipative term has been studied by K. Watanabe. The relationship of this spectrum type and the behavior of the time decay of the solutions has been studied.4. Krein's formula (which is a generalization of the second resolvent equation) was studied by S.T. Kuroda and published5. The finite elements method for the bi-harmonic Dirichlet problems on the polygon in the plane (not necessary convex) has been studied by A. Mizutani.6. The behaviors of the solution at the time infinity for the system of the nonlineat partial differential equations (for example, the coupled Schrodinger and Klein-Goldon) have been studied by A. Shimura and published.7. The regularity and the uniqueness for the initial date problems of the Euler equation have been studied by T. Ogawa and published.8. The scattering theory for the dissipative system has been studied by M. Kadowaki and published.

1. K. Watanabe研究了用算子理论方法处理自伴算子奇异摄动的H-2-结构。作者得到了该算子的一些结果，如嵌入特征值存在的充要条件、散射矩阵的表示等。 2． K. Watanabe 研究了具有界面的麦克斯韦、斯托克斯和纳维-斯托克斯方程的解的规律性。特别是下面的结果是显着的：如果切向分量不具有奇异性，那么解的正则性获得等级1.3。 K. Watanabe 研究了带有耗散项的偏微分方程。研究了该谱类型与解的时间衰减行为的关系。 4． S.T. 研究了 Krein 公式（第二个求解方程的推广）。黑田东彦并发表5。 A. Mizutani研究了平面多边形（不一定是凸）上的双调和狄利克雷问题的有限元方法。6． A. Shimura 研究了非线性偏微分方程组（例如耦合的薛定谔和克莱因-戈登）在无穷大时间解的行为并发表了7． T. Okawa研究并发表了欧拉方程初始日期问题的规律性和唯一性。8． M. Kadowaki 研究并发表了耗散系统的散射理论。